A cantilever from a rectangular cross-section is lying on an elastic Winkler foundation and loaded by distributed loading. The image shows the calculation of the maximum deflection and maximum bending moment.
A tapered cantilever is fully fixed on the left end and subjected to a continuous load q. Small deformations are considered and the self-weight is neglected in this example. Determine the maximum deflection.
A thin rectangular orthotropic plate is simply supported and loaded by uniformly distributed pressure. The directions of axes x and y coincide with the principal directions. While neglecting self-weight, determine the maximum deflection of the plate.
A cantilever from a rectangular cross-section is lying on an elastic Pasternak foundation and loaded by distributed loading. The image shows the calculation of the maximum deflection and maximum bending moment.
A thin plate is fully fixed on the left end and subjected to a uniform pressure. The plate is brought into the elastic-plastic state by the uniform pressure.
A pinned beam with a rectangular cross‑section is subjected to distributed loading and shifted vertically by eccentricity. Considering the small deformation theory, neglecting the self‑weight, and assuming that the beam is made of isotropic elastic material, determine the maximum deflection.
A masonry wall is exposed to a distributed load in the middle of its upper section. The Isotropic Masonry 2D material model is compared with the Isotropic Linear Elastic model, with surface stiffness property Without Tension in the nonlinear calculation.
A cylindrical membrane is stretched by means of isotropic prestress. Find the final minimal shape of the membrane - catenoid. Determine the maximum radial deflection of the membrane. The add-on module RF-FORM-FINDING is used for this purpose. Elastic deformations are neglected both in RF-FORM-FINDING and in the analytical solution; self-weight is also neglected in this example.
A three-dimensional block made of elastic-plastic material is fixed at both ends. The block's middle plane is subjected to a pressure load. The surface plasticity is described according to the Tsai-Wu plasticity theory.
A cantilever with fibers that do not run in direction of the beam axis from a square cross‑section with tensile pressure. Calculate the maximum deflection.
A thin plate is fully fixed on the left end and loaded by uniform pressure on the top surface. Determine the maximum deflection. The aim of this example is to show that a surface of the surface stiffness type Without Membrane Tension behaves linearly under bending.
Determine the maximum deflection of four columns fixed at the bottom and connected by a rigid block at the top. The block is loaded by pressure and modeled by an elastic material with a high modulus of elasticity. The outer columns are modeled as orthotropic elastic material, and the inner columns as orthotropic elastic-plastic material with the same elastic parameters as the outer columns and plasticity properties defined according to the Tsai-Wu plasticity theory.
A spherical balloon membrane is filled with gas with atmospheric pressure and defined volume (these values are used for FE model definition only). Determine the overpressure inside the balloon due to the given isotropic membrane prestress. The add-on module RF-FORM-FINDING is used for this purpose. Elastic deformations are neglected both in RF-FORM-FINDING and in the analytical solution; self-weight is also neglected in this example.
Determine the maximum deformation of a wall divided into two equal parts. The upper and lower parts are made of an elasto-plastic and an elastic material, respectively, and both end planes are restricted to move in the vertical direction. The wall's self-weight is neglected; its edges are loaded with horizontal pressure ph, and the middle plane by vertical pressure.
One layered square orthotropic plate is fully fixed at its middle point and subjected to pressure. Compare the deflections of the plate corners to check the correctness of the transformation.
A three-dimensional block made of elastic-plastic material with hardening is fixed on both ends. The block's middle plane is subjected to a pressure load. The surface plasticity is described according to the Tsai‑Wu plasticity theory.
A two‑story, single‑bay frame structure is subjected to earthquake loading. The modulus of elasticity and cross‑section of the frame beams are much larger than those of the columns, so the beams can be considered rigid. The elastic response spectrum is given by the standard SIA 261/1:2003. Neglecting self-weight and assuming the lumped masses are at the floor levels, determine the natural frequencies of the structure. For each frequency obtained, specify the standardized displacements of the floors as well as equivalent forces generated using the elastic response spectrum according to the standard SIA 261/1.2003.
Four columns are fixed at the bottom and connected by a rigid block at the top. The block is loaded by pressure and modeled by an elastic material with a high modulus of elasticity. The outer columns are modeled by linear elastic material and the inner columns by a stress-strain diagram with decaying dependence. Assuming only the small deformation theory and neglecting the structure's self-weight, determine its maximum deflection.
Determine the maximum deflection of a three-dimensional block fixed at both ends. The block is divided in the middle: the upper half is made of an elastic material and the lower part is made of timber - an elasto-plastic othotropic material with the yield surface described according to the Tsai-Wu plasticity theory. The block's middle plane is subjected to vertical pressure.
A cantilever is fully fixed on the left end and loaded by a bending moment on the right end. The material has different plastic strengths under tension and compression.
A single-mass system with dashpot is subjected to a constant loading force. Determine the spring force, damping force, and inertial force at the given test time. In this verification example, the Kelvin--Voigt dashpot (namely, a spring and a damper element in serial connection) is decomposed into its purely viscous and purely elastic parts, in order to better evaluate the reaction forces.
A cable is loaded by means of a uniform load. This causes the deformed shape in the form of the circular segment. Determine the equilibrium force of the cable to obtain the given sag of the cable. The add-on module RF-FORM-FINDING is used for this purpose. Elastic deformations are neglected both in RF-FORM-FINDING and in the analytical solution; self-weight is also neglected in this example.
A cantilever is fully fixed on the left end and loaded by a transverse force and an axial force on the right end. The tensile strength is zero and the behavior in the compression remains elastic.
A thick-walled vessel is loaded by an inner pressure such that the vessel reaches an elastic-plastic state. While neglecting self‑weight, the analytical and numerical solutions for the radial position of the plastic zone border (under the Tresca hypothesis) are determined and compared.